Among the predicted properties of fractional quantum Hall states are
fractionally charged quasiparticles and conducting edge-states described as
chiral Luttinger liquids. In a system with a narrow constriction, tunneling of
quasi-particles between states at different edges can lead to resistance and to
shot noise. The ratio of the shot noise to the backscattered current, in the
weak scattering regime, measures the fractional charge of the quasi-particle,
which has been confirmed in several experiments. However, the non-linearity of
the resistance predicted by the chiral Luttinger liquid theory was apparently
not observed in some of these cases. As a possible explanation for these
discrepancies, we consider a model where a smooth edge profile leads to
formation of additional edge states. Coupling between the current carrying edge
mode and the additional phonon like mode can lead to {\it nonuniversal}
exponents in the current-voltage characteristic, while preserving the ratio
between shot noise and the back-scattered current, for weak backscattering. For
special values of the coupling, one may obtain a linear I-V behavior.Comment: 10 pages, 3 figure